How do I change the axis reference point of an object?
You need to set the object's origin to the center of the circular base. 

Go into Edit Mode (Hit Tab). In edit mode you can select vertices, edges or faces. To switch the mode to vertices, or edges or faces hit CtrlTab. Select the one that's convenient for you. 

The goal is to have the center vertex on the circular base selected or a loop of edges around the circular base, or all the faces of the circular base. Whichever's center point is at the center of the circular base. Now set cursor position to selected. Use ShiftS. Select cursor to selected. Now exit out of edit mode. Hit Tab. 

Now set the origin to 3D cursor. Use ShiftCtrlAltC. Set origin to 3D cursor. Now you can position the object in reference to the new object origin. Done. :-)